Section 8: Hess's Law

Figure 7-12. Magnesium Ribbon Burning

A strip of magnesium burning. Because the reaction produces intense light, magnesium was the main component of photographic flash powder in the late 1800s. Today, many fireworks contain magnesium because it produces such brilliant white light.

Because enthalpy is a state function (see State Functions sidebar in Section 4), the change in enthalpy of a chemical reaction depends only on the identity and phases of the reactants and products, and not on the specific way the reactants transform into the products. This useful fact is known as "Hess's Law," after Germain Henri Hess (1802–1850), a Russian chemist from the early 1800s. For example, let's imagine a reaction in which reactant A turns directly into product C. The ΔH for this reaction is x kJ per mole.

A → C ΔH = x

Reactant A might also be able to produce C by an alternate route. In this case, A might first turn into B, and B then turns into C. Each of these reactions also has a ΔH value, y and z, respectively:

A → B ΔH = y

B → C ΔH = z

According to Hess's Law, the ΔH of the first reaction (converting A directly into C) must be equal to the sum of the ΔH values of the second and third reactions (converting A into C via B). Expressed mathematically, we have x = y + z.

This allows chemists to figure out the ΔH of a reaction by combining other reactions and adding the ΔH of those reactions together. It is a useful way to calculate ΔH when calorimetry is impractical. For example, let's consider a highly exothermic reaction: the burning of magnesium metal (Figure 7-12):

Mg(s) + $1/2$O2(g) → MgO(s)

To find the ΔH value for the burning of magnesium, we could look up the following information:

Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) ΔH = -459 kJ/mol

MgCl2(aq) + H2O(l) → MgO(s) + 2HCl(aq) ΔH = +141 kJ/mol

H2(g) + $1/2$O2(g) → H2O(l) ΔH = -286 kJ/mol

Note that combining the three reactions and canceling out the chemicals that appear as both reactants and products will produce the reaction for burning magnesium:

Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)

MgCl2(aq) + H2O(l) → MgO(s) + 2HCl(aq)

H2(g) + $\bi1\bi/\bi2$O2(g) → H2O(l)

Because the three reactions "add up" to the reaction for burning magnesium, the sum of the three ΔH values will be the ΔH for burning magnesium:

ΔH = -459 + 141 + (-286) = -604 kJ/mol

The final result is a very large negative number, which makes sense because the reaction is quite exothermic and releases a significant amount of energy in the form of light and heat as the reaction occurs.

Glossary

Hess's Law

The change in enthalpy of a reaction (ΔH) is the same if the reaction happens in a single step or in a series of steps. Thus, the series of steps must have individual enthalpy changes that add up to the total change in enthalpy for the process

Hess's Law

The change in enthalpy of a reaction (ΔH) is the same if the reaction happens in a single step or in a series of steps. Thus, the series of steps must have individual enthalpy changes that add up to the total change in enthalpy for the process